What does physics have to contribute to our understanding and appreciation of beauty?
Name: Anne Dalke (adalke@brynmawr.edu)
Date: 02/10/2005 13:46
Link to this Comment: 12748 |
This week we're reading two chapters from Zee's Fearful Symmetry, Chang's essay on "What Makes an Equation Beautiful," and McAllister's meditation, "Is Beauty a Sign of Truth in Scientific Theories?" All this in preparation for Peter Beckmann's visit to class on Tuesday, when he'll engage us in a conversation about "where the real beauty emerges" for physicists (or @ least for this physicist!). In anticipation of that conversation, post here, please, your thoughts about symmetry, simplicity, and beauty as a sign of truth...
Beauty, Simplicity, Truth...a Complicated Triangle of Debate
Name: Alanna Albano (ajalbano@brynmawr.edu)
Date: 02/11/2005 18:13
Link to this Comment: 12802 |
It's funny...I had never really thought that a physicist would equate beauty with symmetry, because I usually picture mathematicians (as well as artists) being obsessed with symmetry, and physicists being obsessed with equations that explain how the physical world works. The relationship between the concept of symmetry and physics took some getting used to upon reading the essay.
While I'm not sure I'm convinced that ALL physicists equate beauty with symmetry, I am convinced that humans in general do tend to have a preference towards more symmetrical things. For example, I recently watched and participated in a series of dances. Most of these dances, if not all, contained some sort of circular formations. I recall someone pointing out this observation aloud, to which the professor responded that we as humans tend to favor the use of the circle in choreography and dancing. I guess this should not be surprising, since the circle is a rather easy and simple shape to work with.
This leads me to ponder about our use of the circle in other areas of life...we use it without even thinking about it! We circle words or statements in our readings...we circle an important date on the calender...we stir cake batter in a circular motion...perhaps the doodles on the edges of our notebooks contain some sort of circle shape, etc. We seem to be strongly connected to the circle shape. Is this primarily due to its wonderful symmetry, the huge role it plays in our lives, or both?
In reference to Chang and McAllister: While I do agree that a simple-looking mathematical equation or scientific theory can be quite beautiful, I'm still very skeptical of making the connection between beauty and truth, regardless of the simplicity of the equation or theory. From my perspective, a "beautiful" looking theory/equation does not automatically imply truth. I feel that the connection with truth can only be made when that theory/equation has successfully passed experimental tests.
a sense of the mysterious...
Name: Anne Dalke (adalke@brynmawr.edu)
Date: 02/12/2005 10:50
Link to this Comment: 12812 |
Here's a switch for you: Sharon filling in the technical details, while I evoke mystery....
Quite appropriately (for our purposes) The New York Times Book Review is this weekend (2/13/05) featuring a new collection of essays, A Sense of the Mysterious: Science and the Human Spirit, by Alan Lightman, who was an astrophysicist before he became a novelist. The reviewer says that the best essay in the volume is "Metaphor in Science," which gives a "provocative and interesting...analysis of the aesthetics of mathematics, an account of how the subjective idea of beauty can affect the construction of a proof."
Name: Amy Martin (aemartin@brynmawr.edu)
Date: 02/12/2005 11:34
Link to this Comment: 12813 |
I was shocked by the repition of themes of beauty that we had discussed in
class already, and how they came up in the unlikeliest of places (for me
anyways) the "Science" readings. I fundamentally saw all three articles as
dealing with themes of whether something is more beautiful when you have the
learning behind it, or if your gut reaction of if something was beautiful made
that beauty more worthy. I was also struck by the idea of order and chaos and
how they play into
the beauty of science. It seemed to me that Zee's article, in its emphasis on
symettery was constantly refering to an implicit and explicit order of the
universe. This almost blessing that everything is built like it is, and works
has it works. In fact, it felt like Zee was rejecting the idea of chaos as
within chaos he was saying physicits find the beauty, symmetry and design. I
liked his emphasis on the religious because it meshed two worlds that I before
assumed never meshed. I have always thought of science as a rigid, cold,
unsentimenal world which is many ways rejects religious notions of the
miraculous and the spiritual. Yet in Zee's article we see ideas of G-d's
design, and of religious feelings. (p.6) I was also shocked at how much I
related to the readings, Zee's and the article mainly- not the McAllister so
much. Being a staunch humanist who avoids math and science like the plague, I
surprised myself at how like the phyists, I am awed by the design and
symettery of G-d's hand. Reading the Science Times article, I could also
relate to idea of a math equation as beautiful. I loved the idea that math is
using symbols to represent something which with words would be far too
complex. And besides, I'd also found something awesomely simple in the
pythagorean therom and one plus one is two.
One more thought... to me it seemed almost self evident that when we find
something beautiful we immediately think of it as a truth. When McAllister was
discussing the idea that scientists have this innate wish that it'd be so much
nicer if one result to their experiment was true,(p.2), I related this idea
back to that instanteous reaction to things which make them jump out to us in
such an individual and personal way. The opposite of the coin of learned
beauty. It makes perfect sense that there would be such a strong connection
between scienctist and wanted result...
Thining Beauty
Name: Liz Paterek (epaterek@brynmawr.edu)
Date: 02/12/2005 13:22
Link to this Comment: 12815 |
I feel like we limit ourselves when we discuss how to find things beautiful or what is beautiful. Everything must be individual, we must know ourselves. No one should be so arrogant as to believe that they found the perfect way to see beauty or to think they found the truth in beauty. There is no universal method. There is no universal truth. This especially is true when it comes to science. Science cannot give us truth; it gives a possible explaination based on evidence. Therefore if beauty needs some element of truth science must be ugly for it can never provide truth. Yet I enjoy science, I would suppose you could say I find it beautiful. I do not, however, think that truth and beauty are really related in any definatble manner. Everything that a person views is tainted by her experiences and background. We can never escape from the trapping of our mind and see some universal truth. Perhaps it is out there but we cannot show it. If everyone were to see the "universal truth" the world would be incredibly boring. We would lose the individual perspectives that give unique perspectives and make us individuals. On the other hand people feel tricked when they do not see this so called truth and can find science ugly for not providing it. Once again the flaw of individual views comes into play.
I do not think that we can say that complexity or simplicity is beautiful for the simple fact that everything is simple and everything is complex based on tehe level that you look at it. A flower may appear simple but think of all the genetics that went into making, the biological processes it carries out, the atoms that make it up. Using different lenses we can see different things. it's like looking at the form of a picture and seeing simplicity versus looking at the subject and seeing complexity. I felt that way when we did the what is beautiful tests. Many times I worte that things were both simple and complex and was confused on how to answer the question.
Name: Marissa (mpatters@brynmawr.edu)
Date: 02/12/2005 17:25
Link to this Comment: 12819 |
I was really interested by the pieces we read this weekend. I felt that, though they were focused on physics they were quite readable and understandable. I enjoyed the piece by Zee on symmetry. I liked the way that the author was able to point out different ideas about physics and present them in a way that was relatable to everyday occurances like a football game. I relate to the ideas presented, because I usually find symmetric objects as most beautiful. Also the thoughts written about large numbers- I have always been facinated with my own inability to grasp extremely large numbers abstractly. Especially once I'm up to the billions, trillions, or the mother of large numbers, infinity, I lose all grasp and am forced to resort to "a lot."
I liked that the McAllister article showed how different physicists thought, placing a name and a concept to the different theories about beauty as related to physics. It was also interesting to see how the scientists were at times "compelled to abandon their longstanding aesthetic preference for determinism and visualization" (8) and the effects this had on physics. These readings were a very interesting look into something I've never given much thought to, beauty in physics. I am looking forward to discussion on Tuesday relating to this.
Beauty vs. Truth
Name: Annabella (annabellawood@yahoo.com)
Date: 02/12/2005 18:38
Link to this Comment: 12820 |
I found the argument that beauty in science does not equate to truth very compelling. After all, if an absolute definition of beauty can not be pinned down and agreed upon by all, and truth is agreed upon by all by definition, then the two can not possibly equate by any stretch of the imagination.
But what if truth can can be influenced by the imprint of our belief of it, much as quantum physics has determined that nothing can be observed without being changed by the act of observation? What if there is no absolute truth, but the one each individual holds as true? What if the truth is actually relative and not absolute?
As an example of this possibility, consider the simple auto accident. If there are three witnesses, the police officer will usually get three different accounts of what happened, and each will be true to the witness who believes it. What is the truth of what happened? Is there an absolute truth that none of them experienced? If none of them experienced it, would it be truth? Or could the belief of each witness have imprinted the truth and altered it slightly, thereby making it appear as something different to each one?
With truth defined thusly, beauty can equate with truth in the sciences as well as the rest of life. After all, who would want the truth if it meant giving up beauty? If they were mutually exclusive, which would you choose to experience? I would choose beauty, for truth without beauty would render life barren.
Fortunately, I have found in my own experience that my search for truth has led me to an ever increasingly beautiful world. I find that beauty is the deepest truth this life has to offer.
beauty and symmetry
Name: Rachel Usala (rusala@brynmawr.edu)
Date: 02/12/2005 20:01
Link to this Comment: 12822 |
Anyone who has taken a class in physics, chemistry, biology, or any other science cannot deny the beauty and surprise of nature's symmetry.
Nevertheless, I've read some about the theoretical physicists' goal of creating "The Theory of Everything," and am frankly stymied why we are trying to make a theory that cannot be empirically proved. The optimistic statement of Zee that we are perhaps getting close to finding a unifying theory, that can explain all the physical phenomenon of the universe, reminds me very much of the sentiments at the turn of the 20th century. And wow have we learned an enormous amount since then! I've read most of "The Elegant Universe" by Brian Greene that is mentioned in the readings, and string theory sounds very much like a fairy tale to my untrained ears. Shoudn't we finish calculations to unify the theory of QED with the strong force before we throw gravity into the mix and unify all the theories? I am, at heart, a scienist but even I don't believe everything can be bottled into one theory of symmetry and simplicity. There is a spirtuality to life that science is not capable of explaining.
I found the discussion by McAllister of the dilemma of a scienst to use his or her aesthetic judgement in assessing whether a theory is true very interesting. I think of aesthetics as a tool for creativity, but not a criterion for truth. To me, beauty has a place in science as a guide for inquiry but not as a label of certainty. The argument is made by McAllister that scientists' aesthetic preferences are culturally acquired. For me this was the fatal blow to the argument that beauty is scientific truth. Culture is dynamic. Aesthetic preferences change with the times; the laws of physics, if scientific evidence so far is right, are not.
Physics and Beauty
Name: Meera Jain (mjain@brynmawr.edu)
Date: 02/12/2005 23:52
Link to this Comment: 12823 |
On Saturday I took a solo trip to the Barnes museum ( I was unable to go with the class before) and was blown away by the amount of art, the way it was displayed and how close BMC is to such a great place! I liked art, but got impatient when I visited museums and this time (maybe because I'm older) I sat down on the benches and just let the pieces form thoughts in my mind. After seeing so much Renoir, I love his depiction of women and families. I really liked Modigliani sp? painiting of faces, they are very slim and sharp. It was nice to be there by myself and take my own time in the museum. It was amazing to see these beautiful pieces mixed in with silver art hung on the walls, and that each room would lead into another and so on.
After visually experiencing beauty if was interesting to read these assignments and see how I think like a physicist. Although I deteste science, I definitely agree with Zee and that beauty is based on symmetry and reflections. All of Renoir's pieces were of faces and people who had perfect bodies (2 legs, 2 arms, 2 eyes, etc. all of equal size) and that would never change if I rotated them. I like the Lillies painting by Manet because there are an equal number of petals all around a common center.
However, this is my TRADITIONAL view of beauty. And who is to say that a something that is not symmetrical- is not traditional? I guess my symmetry obsession comes from society and things I read and movies I watch.
In the NYT article, I loved the last paragraph about the child's understanding of "1+1=2" being a beautiful equation. I would say that at that moment, the experience was beautiful. A small child grinning and holding up his small fingers to explain his thinking process.
In McAllister's article, I found it difficult to comphrehend how beauty makes a theory true and how asthetic judgement plays a role. Maybe someone can clarify this point in class for me?
"Real beauty has nothing to do with colorful pictures?"
Name: Katy McGinness (kmcginne@brynmawr.edu)
Date: 02/14/2005 00:37
Link to this Comment: 12867 |
I totally disagree that real beauty has nothing to do with colorful pictures, of course, but I find the idea that one can find something beautiful in what is considered the hardest of all sciences--namely physics--interesting and intriguing. It was precisely the hardness of physics that caused me to hate it so much when I took the course as an eleventh grader. I can understand the beauty of chemistry--creating substances and reactions that can be beautiful in terms of sight, sound, etc. As a high schooler I far preferred chemistry to physics. But physics being beautiful? It seemed like an oxymoron and quite impossible until I read these articles. While I personally cannot see myself finding something inherently beautiful with physics, I also recognize that physics just isn't my thing. People for whom it is their thing may find something heartbreakingly beautiful about it. I think we all find something beautiful about the things that we are passionate about, and physicists are no exception. Just as the musician finds his guitar licks beautiful and the painter finds his mixture of colors aesthetically overwhelming, so too can the scientist find her newly discovered theory of motion something truly and inescapably beautiful.
Name: eebs (elchan@brynmawr.edu)
Date: 02/14/2005 11:17
Link to this Comment: 12875 |
i must admit, the first thing that popped into my mind during the reading was the title, "fearful symmetry". although i found the entire essay by Zee very interesting, i couldnt agree with him when he said that physics was beautiful.i understood the entire portion of the essay that talked about balance and symmetry being very simple yet beautiful in nature (for they exist in great numbers). when zee talked about the circle being the most aesthetically pleasing, i started to think if all cultures thought the same way. i started to think about flags, a symbol of one's country and how most flags are bands of color, or they posess some sort of rotational symmetry, just like the circle. maybe zee has a point, although some people may not see beauty in everything that is symmetrical, they probably feel some sort of aesthetical pleasure when they see that something is balanced.
in the article about equations, i thought of it also being a way of balancing things- one side balancing another in what we now call an equation. for those who dislike math, they dont find beauty in the equation, but they might find beauty in the concept of an equation since it represents balance. i personally have a love-hate relationship with equations; i am amazed by how the two seemingly unequal sides are equal, but then again, the thought of having to do math .. well, scares me a little.
im not a very religious person, but i do believe that there is some form of higher power that is in control of us and our surroundings. in nature, we see all sorts of mathematical sequences, patterns and ratios that makes everything beautiful- from all of natures' fibonacci sequences/paterns, to the golden ratio of the human face-- something that is geometrically or mathematically 'beautiful' is probably created like that on purpose.
science and beauty
Name: Alice (astead@brynmawr.edu)
Date: 02/14/2005 14:08
Link to this Comment: 12877 |
I keep asking myself the question: do I think science is beautiful? After thinking about it, I think I can answer yes to that question now. I think the mystery and complexity of science is beautiful, and the fact scientists have found ways of understanding the mystery is amazing. I know some people have said they would rather have Dewey-esque experiences, without any outside knowledge, but I think science is one place that having background knowledge makes us appreciate the beauty more. I think I struggled with that question because I cannot look at an equation and think it beautiful because it is symmetrical, but I realized that what is beautiful is what it represents.
I think A. Zee poses an interesting idea that the "Ultimate Designer would only use beautiful equations in designing the universe." At first, I fouund it a little bit confusing that some scientists would choose something they found aesthetically pleasing as a truth rather than an ugly equation. However, when I read the clip about the most beautiful equations, it sort of made more sense to me. All of those equations are very simple. I guess those equations are beautiful to people because they take something so large and difficult to understand and put it in this small, simple equation. I think A. Zee makes a valid point that nature must have an "underlying design of beautiful simplicity." However, I am not a scientist, so it is easy for me to say that.
beautiful equations
Name: Malorie (mgarrett@brynmawr.edu)
Date: 02/14/2005 15:17
Link to this Comment: 12880 |
The article "What makes an Equation Beautiful" really spoke to me as the to be possibly math major that I am. I agree with the article, I love to see large things condensed into smaller ones. Part of it is laziness, someone once told me that Mathematicians were inherently lazy which is why they have sort hands for everything, but there is also the joy of saying that a bunch of words and symbols can be expressed in just one or two. I know that one equation that I have found beautiful and helpful over the last year is the equation sin^2 x + cos^2 x= 1. I love it when I'm working on a problem and I can see that I'm going to get sin^2 x + cos^2 x, or something similar that I can easily replace. When I think about it, I remember that I do often say thing as I work on math such as "thatÕs ugly" or I may exclaim "Beautiful!" when an equation works out. It just feel so good to solve a problem, its beautiful experience for me.
Another thing I wanted to mention is Fractals. I love Fractals. I think they are beautiful and cool. I'm not sure exactly what they are, I could not give you a definition, but I know that they are equations that can be represented physicals as pictures and, so I have herd, music. They are Series of numbers- where you perform the same operation over and over again, using the information you got previously to solve the next one. I just think it's so beautiful that you can explain something visual like that mathematically, just like how A. Zee finds the physicals laws of rain beautiful as he looks at a rainbow.
physics sculpture
Name: Flora (fshepher@brynmawr.edu)
Date: 02/14/2005 15:29
Link to this Comment: 12881 |
When I graduate, I will have the choice between being the fourth generation scientist in my family or the fourth generation artist (artist meaning any discipline). These are the only two disciplines that really interested me. Growing up, I switched from training in one arts discipline to another, covering everything from accordion to stage fighting. Now, in college, IÕve settled down into physics, which seems, to my family, worlds away from my childhood. This situation causes me to think through many of this issues presented in these articles (having already read Zee) often. How do I know that physics is true and/or worthwhile? Why do I find these theories so beautiful? What is it about physics that makes me miss problem sets over the summer? And to explain it to much of my family, I have to phrase these answers without the luxury of ChangÕs equations.
First of all, it doesn't surprise me anymore that the language of physics overlaps so much with the language of art. I feel like both disciplines are creating something. I'm sure other scientists in other disciplines may feel the same way, but I find physics more all-encompassing.
As for McCallisterÕs arguments, I think I agree with him that more than just empirical success causes a theory to be true and that beauty can have something to do with it. But just as weÕve discovered in class, finding what the beauty is is tricky, as he showed with examples from history. And I think thatÕs part of what intrigues me about physics. At any time, we could find something that doesnÕt fit in the theories yet and then have to remodel everything to form a more perfect (and thus, more beautiful?) system.
I guess, to me, physics is beautiful because itÕs sort of a huge mental sculpture of the world. ItÕs not an accurate replica of our world, but it models the world as best it can. And I think PeterÕs correct. Pictures have little to do with it except maybe to help you see the sculpture a little better. And the equations have little to do with it. All the textbooks are just representing something bigger an infinitely beautiful.
Beauty in Math and Science
Name: Kara (krosania@brynmawr.edu)
Date: 02/14/2005 15:39
Link to this Comment: 12883 |
I loved the article on what makes equations beautiful. This, I'm sure, is not surprising since I'm a future math major, but equations for me sort of embody what beauty really is. You look at an equation, and its a summary of a very complicated idea compacted so that your mind can grasp it all at once. If you think about it, a beautiful painting is the same way. It is one picture that summarizes very complicated themes and emotions all at once. You look at a painting and you are overwhelmed by how many different ideas it can evoke. That is what a beautiful equation does for me. I can look at it as many times as I like, and each time I will see a different aspect of what it represents. And yet, it can be so simple and take up no more than a line on a page.
I especially loved the ending quote about Harrison's son and his reaction when "he saw that the tweo fingers, separated by his whole body, could be joined in a single concept in his mind." That is the other truly beautiful thing about equations, that they can summarize a relationship between two otherwise unconnected things. Anyone who sees beauty in relationships should be able to appreciate that.
I found the other two articles on beauty in science a little tedious. Both writers made the assumption that everyone sees beauty in symmetry and simplicity. This is definitely not always the case, and its also not always the case that beautiful natural phenomena are simple or symmetric. I was frustrated byt he first article because it kept referring to a more detailed explanation of what he was talking about in later chapters, which we were unable to read. The last article frustrated me because I couldn't understand why I should care whether truth and beauty are the same. I don't know how anyone could make the assumption that because something's beautiful that means it must be the truth, so I wasn't much interested in learning why this belief was false.
Feng Zee
Name: Elizabeth Newbury (enewbury at brynmawr.edu)
Date: 02/14/2005 16:11
Link to this Comment: 12885 |
I found Zee's argument to be very compelling. I'm not a philosopher or theologist by any stretch of the imagination, but I couldn't help but be reminded of the same concepts of the 'beauty of simplicity' in a lot of Eastern religions or ideologies, like Feng Shui. Get rid of the clutter, get rid fo the mess, try to see the beauty that's laid bare. Often times we get bogged down with trying to add to make beauty. But now, forget the chess and football and embrace the Go.
"The ability to simplify means to eliminate the unnecessary so that the necessary may speak." -- Hans Hofmann
And from the scientific point of view, from the physics point of view, some of the most beautiful equations are where science has managed to boil down years of observation into a single, simple, brief forumla. What makes these equations beautiful? According to Zee, it's because of some connection that the Creator or Nature, while filled with millions of different complex structures, was comprised of very simple rules. So when a scientist manages to find one of these simple rules to the Go game of life, there is not only a sense of pride but also a sense of beauty.
"Making the simple complicated is commonplace; making the complicated simple, awesomely simple, that's creativity." -- Charles Mingus
But I really wonder if Nature is that simple. If you have so many different individual structures operating at the same time, whether atoms or photons or organisms, can they really be boiled down to a simple little forumula? Whatever happened to the chaos theory? The equations that scientists come up with are, in truth, based on extensive research. But what if there is one instance where the apple does not fall, but instead floats away? Where was gravity? What then happens to the forumla?
I think I'm swinging on a bit of a tangent here, but to push it further -- science is a belief system, nearly a religion. Why are these simple equations so beautiful? Because of the child's joy when he learns 1+1=2? Because of their history? Because of what they stand for, both in the realm of science but also in the realm of history? Or do we just learn that they are, indeed, beautiful things? I don't think that these equations would be as beautiful to a person from a society not so dependent on science.
But I digress. All in all, I agree with the premis of Zee. Nature is beautiful, for both its complexity but also its inherent simplicity. It's also beautiful to have a 'why' answered by a 'how'. I can't explain it, but there is something comforting, something enjoyable, something beautiful about knowing how a green leaf is green, and how a rainbow is formed. It doesn't matter if it's science, though -- I'd be just as content if you told me that the reason for a rainbow is because a giant bird streaked across the sky and those were it's tail feathers. Perspective is everything.
Comments to Reading
Name: Jaya (jvasudev@brynmawr.edu)
Date: 02/14/2005 16:15
Link to this Comment: 12886 |
At first I was a little bothered by the excerpts from Zee's book. He talked about how real beauty can be found in the fundamental laws that govern life, that the underlying design would reveal why a certain something is so beautiful. My question for him is, if you ever do find the real underlying design, would the object still be beautiful? It made me think of the idea that we've discussed in class over and over how knowledge taints someone's vision of beauty. Personally, I find beauty in NOT knowing the underlying design because it makes you appreciate the unanswered complexities of life even more; I'd just rather leave them alone.
But after reading the New York Times article, I had a better appreciation for his excerpt. The idea that a jargon of symbols, numbers, and equations can explain the universe in such a simple way is truly a magnificent thing, and something that I didn't think about before. The same applies to mathematicians, chemists, physicists etc. line of work- discovering ways of making sense of the world must be a very beautiful thing to them.
However, I did not like how Zee or McAllister made beauty seem like an obvious thing, especially McAllister, when he said "it is not difficult to assess how beautiful an object is." I got irritated by reading this statement- beauty is far more complex than symmetry, simplicity, scientific theory, etc.... if it really was this simple, then I wouldn't be in this class right now, now would I?
Sure, it's pretty, but does it exist?
Name: Alice Kaufman (ajkaufma@brynmawr.edu)
Date: 02/14/2005 16:16
Link to this Comment: 12887 |
The articles raised some concerns I have for the ÒtruthÓ in physics. Because there is an active choice in what physicists call true, and thatÕs simply if the math looks prettier (Peter Beckmann may say as much tomorrow, since IÕm pretty much directly quoting him). Other explanations for phenomena may work just fine, but certain equations and concepts are much less messy to work out. Unfortunately, there is no guarantee that the universe is designed to be mathematically simple and tidy. This isnÕt a big problem for me; after all, as children weÕre taught that life is seldom fair. But it does create a problem if we want to know fundamental truth, which is, some would say, the point of physics. This method of picking the neater equations for explaining the universe virtually guarantees that we canÕt get to any fundamental truths; we can only get a rough, sketchy kind of idea, based on concepts that most phenomena agree with. ItÕs impressive that weÕve made progress (well, new ideas that fit phenomena better) at all. ThereÕs a sort of doomed romanticism about it all.
Something like 'Sisyphus' may be a harsh, overly simplistic analogy, but the Sisyphus was beautiful too. My perspectives may change if I can learn all the math that goes along with physics. But right now, my ignorance creates a nice, comfortable barrier between what I'm a little scared of and what I believeÐthese equations werenÕt chosen at random, and they certainly werenÕt picked because theyÕre more beautiful. Look at all those imaginary numbers and partial differentiations! ThatÕs just ugly. There has to be a reason that this works, it must be true. If I learn all the math, it might start looking prettier, and then thereÕs more room to doubt.
I have is an even bigger problem, though. Can we start with basic axioms to prove something? Can we pick any starting point and say Òthis is real, this is true?Ó I know that physics now starts with experimental data, but how do we know that the data we collect isnÕt affected by us? Logic puzzles are very beautiful to me, and math (that I have the resources to understand) is as well; I just canÕt say that they prove a truth to me.
Symmetry
Name: Catherine Davidson (cdavidso@brynmawr.edu)
Date: 02/14/2005 16:17
Link to this Comment: 12888 |
In the section called Spring Redux, Lee reminded me of the idea we have been discussing in class about whether knowing about something makes it more or less beautiful. Lee write how beauty is found in simplicity...and that there are many types of symmetry. He claims physics to be the most reductionistic science and tells the story of protons and electrons. Instead of explaining to a child the whole process of why leaves are so green in the spring, it suffices to explain how electrons and protons interact with eachother. Also, in talking about nature's beauty, and how people find more beauty in symmetry, it just so happens that the interaction between electrons and protons is "completely fixed by a symmetry principle". Cool.
Although I do enjoy science and math - to an extent - I find physics overwhelming. However, I appreciate how it can either be very complex or very simple and that, as Chang mentioned in his article, very complex life processes can be explained using one equation. At the same time, I dont like the idea of reducing beauty to equations or theories. I dont think beauty can be constrained by science. Sometimes knowing the simple process or reaction behind a rainbow may make it more beautiful. Sometimes just appreciating the colors plain and simple are just as beautiful, if not more beautiful.Im curious to know how we perceive symmetry and if what we find beautiful individually happens to be similar in symmetry.
Physics and Beauty
Name: Krystal Madkins (kmadkins@brynmawr.edu)
Date: 02/14/2005 16:22
Link to this Comment: 12889 |
I thought that the readings this week tie in nicely with what we have been discussing in class and also brings focus to where many people probably don't look to find beauty...mathematics and science. All of the articles seemed to note simplicity and truth as basis for something being beautiful. This ties in with all the discussions we've had in class about whether or not knowledge plays a role in what we find beautiful. It also goes along nicely with last week's readings where simplicity and complexity in relation to beauty were also discussed as well as how the narrative and the journey to the 'answer' lends beauty to science. I thought the emphasis placed on symmetry in regards to beauty was also very interesting. I know that the articles meant it mostly in regards to equations and physics but I kept thinking back to a show I saw on tv about what makes a person beautiful. If I recall correctly, people with more asymmetrical faces were deemed as less attractive than people who's faces showed more symmetry. I think it's awesome how the ideas of symmetry, simplicity, and truth can account for beauty across so many different areas (science, paintings, music, mathematical equations). I also thought that the idea that something beautiful seems more truthful was interesting. I experience this sometimes in science and mathematics classes where the equations that look more simple or more 'beautiful' seem more truthful to me. It's just a gut feeling I have. It also ties in to some studies I've seen where the findings indicate that more attractive people (along with youthful looking people)will be viewed more often as telling the truth than a less attractive or young counterpart who is telling the same lie. I really think that this overlapping explanation for why people find certain things beautiful is amazing.
Natural Beauty
Name: Amanda G. (aglendin@brynmawr.edu)
Date: 02/14/2005 16:28
Link to this Comment: 12890 |
Fundamentalist physicists apparently claim, "Let us worry about beauty first, and truth will take care of itself!" Physicists are driven not only by precision but by aesthetics and have learned that "Nature, at the fundamental level, is beautifully designed." The author of "In Search of Beauty" writes about the beauty of the perfect spiral of a chambered nautilus. There's the beauty of waves caused by physics as well as the beauty of a single snowflake. Natural beauty is found in our "designer universe." Physicists study this so that the rest of us can understand.
We are told that symmetry is beautiful. A baby is said to stare longer at a symmetrical ("beautiful") face than an assymetrical ("ugly") face. That natural urge to find beauty in daily life can be met by equations, such as the physicists, or by just emotions that stem from the beauty. The equations have proved that symmetry is beautiful. Despite this, I wonder, why a number of "beautiful" women have slighttly assymetrical characteristics. Cindy Crawford has a mole and some models have crooked teeth. Does the simple distraction of the exact symmetry make something even more beautiful? Or does it just make it more interesting?
The simplicity of symmetry is what is thought to be beautiful. Physicists see this in nature. "Nature's rules are simple, but also intricate: Different rules are subtly related to each other. The intricate relations between the rules produce interesting effects in many physical situations." These rules can be applied throughout the universe. Aesthetics really does influece more than we think.
Name: Mo Rhim ()
Date: 02/14/2005 16:52
Link to this Comment: 12891 |
I thought that the readings for this week were very interesting but not compelling at all. I was initially and probably quite unfairly turned off the Zee essays mostly because of her writing style. I found it to be oddly pretensious like in her metaphor using the opera when she is trying to describe in her writing about the fundemental simplicity in nature and the broad design of the world. What is a libretto? I also was immediately skeptical of her authority or believability because she said that when she looks at two equations, she automatically goes for the one that appeals to her aesthetic sense rather than trying to figure out which equation would be most appropriate and correct. I do not believe that you can "worry about the beauty thing first, and the truth will take care of itself" especially in science fields. Those were the initial things that turned me off intially and though I do admit I did not find her writing style all that simple in terms of being able to follow her train of thought I do agree with the fundemental principle that she is arguing for: nature can be beautiful in its simplicity, which gives rise to a more complex matrix of order. I think that nature can be very simple in its design and I liked her use of the famous japanese painting of the waves and the micro picture of a snowflake. THe comparison showed the micro and macro levels of looking at fundementally the same thing or substance. I am not saying that I completely disagree with everything that Zee and Chang had to say in their writing, but I am definitely not a convert to their way of thinking.
I liked it when McAllister said that it is not difficult to assess how beautiful and object is because we can make that judgment and their is no danger of "subsequent discoveries" overturning the verdict. I liked the value and trust placed upon individual judgment of the aesthetic However, I still cannot quite believe that we could use our aesthetic senses to find out how close scientific theories are to the truth. This simply does not seem reliable to me. I know that if it were up to me, I would have discounted every Calculus problem and theorem in my senior year of high school. I would have proven them to be untrue in my head. But that is not the way that we function and it is not the way that we think. I do like McAllister's argument the most because it does allow for some loopholes like that the truth and undeniable repeated empirical success can over time make something more beautiful. This is what stood out in my mind as true. Perhaps it is not beauty then truth, but rather, beauty follows truth. We see beauty in things that we can KNOW to be true. Truth first, and beauty will ultimately follow.
Beauty in Math and Science
Name: Tanya Corder (tcorder@brynmawr.edu)
Date: 02/14/2005 17:00
Link to this Comment: 12892 |
James McAllister appeared to begin with one argument, but after attempting to support it, his train of thoughts ended up at a conclusion that seemed to disprove his argument. However, he slyly readjusts some of his ideas to make it appear as though he indeed is still claiming the same argument. He started off arguing that beauty is a verifying factor for scientific theory and can be advantageous when empirical data cannot be attained or when empirical analysis proves inconclusive. Then he attempts to prove his theory by using ÒempiricalÓ means. ÒAll such statements presuppose that beauty is indeed a sign of truth in scientific theories. But what is the evidence for this proposition? Ó (2). He tries defining aesthetic properties using Òempirical testsÓ (3), but this proves inconclusive so he takes another approach: assuming Òaesthetic properties that are a sign of truth in theories are those exhibited by the world itself.Ó This too proved inconclusive, because he thought that theories with aesthetic value are what make us deem the phenomenon they are describing as beautiful in the first place. A third attempt to define aesthetic qualities led him to the path that disclaimed his initial argument. He states that theories that Òbuilt up their impressive empirical track recordÉcame gradually to be seen as aesthetically pleasing.Ó So heÕs saying that we should use beauty instead of experimental information to determine the validity of theories, but that theory is not deemed beautiful until it has experimental backing. Therefore, beauty does not really give you information about the truth of the theory, it is just what you call a theory that has been proved true by experimentation.
Now, after being a little critical, I will comment on how I was pleased with the article by A. Zee and the article on the beauty of equations. I really like how Zee took a firm standpoint when stating that it is the symmetrical and simple interpretations that tend to explain nature and natural events. I agree, and I love the quote he inserted from Einstein: ÒI want to know how God created this world. I am not interested in this or that phenomenon, in the spectrum of this and that element. I want to know his thoughts, the rest are details.Ó I feel like that is a great way to attempt to explain scientific phenomenons in nature. Most things in nature have proved to be harmonious, interdependent, and dichotomous. Someone created everything so that it could all fit together with purpose. The questions I would ask myself would be ÒWhat was GodÕs purpose when making this or that?Ó For example, if I was to create a world that needed to run as efficiently as possible, and needed to meet certain criteria, how would I do it? Simplicity, balance, and the perfection of symmetry tend to be reasonable characteristics of that world.
The article on equations was cute. I love looking over my math homework after I finish because I find it to be the most beautiful homework I turn in (This sounds weird, so IÕll probably bring in a sample HW to prove how beautiful it is). It possesses graphs, equations explaining those graphs, and very few words - which I find to be the most beautiful aspect. I found all of the responses to why certain equations were beautiful justifiable. However, personally I find equations in general beautiful because they tell us so much about the behavior of different variables in the real world, and they can be easily manipulated to help you find whatever information you want.
Last Tuesday's Class
Name: Rebecca Donatelli (rdonatel@brynmawr.edu)
Date: 02/14/2005 21:14
Link to this Comment: 12897 |
While sitting in class last TUesday I was disturbed by the conversation going on. We were discussing Dr' B's presentation on light and colors. Many people did not know that the way colors of light are created is diffent then the way colors of pigment are created. I didn't find that outrageous becuase different schools and teachers all hvae their own unique curriculum. However, what I did find upsetting was the fact that certain people felt upset or betrayed when they acquired this new knowledge.
It is not that this new knowledge contradicted what they alrady knew but in my opinion it enhanced it and broadened it and that I find to be beautiful. It seemed as though in feeling betrayed by this new information that they were closing themselves off. All through out our education and even after we are constantly learning that things are not as we once thought. To feel betrayed and to possibly refuse to accept new knowledge seems like an unnecassary and kinda sad loss. After all it seems as though the majority of our education calls us to see things in ways we haven't seen them before and that in turn makes for more well-rounded individuals.
Name: Brittany Pladek (bpladek@bmc)
Date: 02/15/2005 01:09
Link to this Comment: 12905 |
In McAllister's essay, he writes that "scientists' aesthetic preferences respond inductively to the empirical performance of theories... scientists attach aesthetic value to an aesthetic property roughtly in proportion to the degree of emprirical success scored by the set of theories that exhibit the property. If a property is exhibited by a set of empirically very successful theories, scientists attatch great aesthetic value to it, and thus see theories that exhibit that property as beautiful."
What strikes me about this statement is how universal it is. It seems to me that McAllister's just pointing out the human tendency to initially resist new ideals of beauty before gradually accepting them. For a random example (pulled from the book I have closest to me), when the Symbolist movement started in 1880s Paris, lots of critics (and poets!) had hissy fits. But then everyone settled down and accepted the movement, and eventually its principals came to embody the new vogue of "beautiful poetry," (and some of its poets got so famous that unfortunate movies starring Leonadro DiCaprio were made about their lives). Same goes for painting. Didn't a lot of art critics initially scoff at Picasso? And according to McAllister, same goes for science. Quantum theory was considered hideously ugly... until it started working, and came "gradually to be seen as aesthetically pleasing."
So maybe it's less that "beauty is truth, truth beauty" and more just "truth is beautiful." Truth, or stuff that's empirically "proven" to be true, exhibits an attractive quality to scientists. Maybe there is no inherent "quality" of beauty in the realities of the universe. Maybe humans just think it's cool when Stuff Works and We Know Why, and it's the clarity that our own intellects apply to the universe's physical properties, not those properties *themselves*, that is truly beautiful.
Revised Assignments for Next Week
Name: Anne Dalke (adalke@brynmawr.edu)
Date: 02/17/2005 13:19
Link to this Comment: 12967 |
Revised Assignments for Next Week
No forum postings due this Monday (because papers are due Wednesday!)
For Tuesday, 2/22 read
Philip Fisher's "The Rainbow and Cartesian Wonder" and "Wonder and the Steps of Thought."
Give yourself the gift of 1 1/2 undirected hours on Tuesday morning of "being hyperaware" of the world: go wandering (not seeking) and see what you can find.
By 5 p.m. Wed, 2/23, post on-line your second 5-pp. paper, on "Seeing Beauty as a Scientist." Then spend an hour or two, Wednesday evening, reading through some of your classmates' posted papers, which will be available @ Web Papers 2 Forum. Please also bring a hard copy of your own essay to your small group session on Thursday morning (submitted in a folder which includes your first marked essay).
"Seeing like a scientist" can take the shape of a number of different sorts of papers:
designing matter(s)
Name: Anne Dalke (adalke@brynmawr.edu)
Date: 02/17/2005 17:36
Link to this Comment: 12980 |
Sharon and I have a colleague in the Chemistry Department @ UVA, Cassandra Fraser, who is coordinating a university-wide collaborative course on Designing Matter that--on a far larger scale--has some interesting resonances w/ our class on "Beauty." Cassandra just called my attention to what she did on the web this week w/ The Gates, as well as to a quotation about the metaphoric quality of writing, and the creative act of discerning patterns within it, that might help inspire your writing assignment for this coming week.
"A Lot of Knowledge Is Dangerous, Too"
Name: Anne Dalke (adalke@brynmawr.edu)
Date: 02/21/2005 22:46
Link to this Comment: 13092 |
This was the title for a review article in the New York Times this weekend (2/20/05):
Where is the ideal synthesis between knowing next to nothing in advance about a work of art, and hence appreciating it fresh, "on its own terms," and so overpreparing that all kinds of inappropriate criteria distort one's perceptions?....There are compelling arguments for appreciating an artwork on its own terms....but the sedimentary texture of knowledge, the layerings of appreciation, can provide pleasure on a first encounter, too....one set of perceptions does not, cannot, invalidate another....Perhaps the trick is not to know nothing but to know as much as possible and then, somehow, to set that knowledge aside, encounter the work afresh and finally bring knowledge back to bear on what we have seen and heard and felt.
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